We can use fraction models to understand how to multiply fractions.
For example, let's suppose that we wish to compute the following product of fractions:
Let's start by representing using a square fraction model, like the one below. Notice that we have split the fraction vertically.
Since we need to multiply the above fraction by , we split the whole into equal parts horizontally. This way, each of the original pieces is split in half. Then, we only keep the shaded pieces in the bottom row.
From the picture on the right, we see that the shaded part represents of the whole.
Therefore,
Notice that we can simplify this answer further by dividing the numerator and denominator by However, in this lesson, we'll focus just on multiplication and not worry about simplifying the final answers.
What multiplication problem is represented by the model above?
We have on the left and on the right.
Therefore, the multiplication problem shown is:
What multiplication problem is represented by the model above?
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a
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$\dfrac{2}{3} \times \dfrac{1}{2} = \dfrac{2}{6}$ |
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b
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$\dfrac{4}{3} \times \dfrac{1}{2} = \dfrac{2}{6}$ |
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c
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$\dfrac{1}{3} \times \dfrac{1}{2} = \dfrac{1}{2}$ |
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d
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$\dfrac{2}{4} \times \dfrac{1}{2} = \dfrac{1}{2}$ |
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e
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$\dfrac{3}{2} \times \dfrac{1}{2} = \dfrac{6}{2}$ |
What multiplication problem is represented by the model above?
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a
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$\dfrac{2}{4} \times \dfrac{1}{4} = \dfrac{2}{12}$ |
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b
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$\dfrac{1}{3} \times \dfrac{1}{4} = \dfrac{4}{12}$ |
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c
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$\dfrac{1}{3} \times \dfrac{1}{4} = \dfrac{1}{10}$ |
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d
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$\dfrac{2}{3} \times \dfrac{1}{4} = \dfrac{2}{12}$ |
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e
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$\dfrac{2}{3} \times \dfrac{1}{4} = \dfrac{1}{12}$ |
What number is missing from the multiplication problem below?
We have on the left and on the right.
The shape on the right-hand side is split into equal parts by horizontal lines. So, the shaded part on the left is times larger than the shaded part on the right.
Therefore, the multiplication problem shown is:
So, the missing number is
What number is missing from the multiplication problem above?
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a
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$5$ |
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b
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$4$ |
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c
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$6$ |
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d
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$3$ |
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e
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$2$ |
What number is missing from the multiplication problem above?
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a
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$3$ |
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b
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$8$ |
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c
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$6$ |
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d
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$4$ |
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e
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$5$ |
What picture is missing from the multiplication model below?
In the model, we have on the left.
Since we are multiplying by , we need to split the whole into equal parts horizontally.
From the picture on the right, we obtain that the shaded part represents of the whole.
The missing picture is:
What picture is missing from the multiplication model above?
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What picture is missing from the multiplication model above?
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Use the model above to calculate
Since we need to multiply by , we split the whole into equal parts horizontally.
From the picture on the right, we obtain that the shaded part represents of the whole.
Therefore,
Use the model above to calculate $\dfrac{3}{4} \times \dfrac{1}{2}.$
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a
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$\dfrac{1}{4}$ |
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b
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$\dfrac{3}{2}$ |
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c
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$\dfrac{3}{8}$ |
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d
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$\dfrac{1}{8}$ |
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e
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$\dfrac{3}{4}$ |
Use the model above to calculate $\dfrac{2}{3} \times \dfrac{1}{4}.$
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a
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$\dfrac{2}{3}$ |
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b
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$\dfrac{1}{12}$ |
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c
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$\dfrac{1}{3}$ |
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d
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$\dfrac{2}{4}$ |
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e
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$\dfrac{2}{12}$ |
